anonymous
  • anonymous
Gasoline is pouring into a cylindrical tank of radius 3 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.2 ft/sec. How fast is the volume of gasoline changing at that instant? Round your answer to three decimal places.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Okay, you can find the volume first since you have h and r , so : \[V = \pi r^2 h\] \[= ( 3)^2 (6) \pi\] = 169.65 ft^3
anonymous
  • anonymous
sstarica, isn't this the same thing we were tackling
anonymous
  • anonymous
now find V' which is :\[V' = 2\pi rr'h'\]

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anonymous
  • anonymous
not really @iam , somehow similar :)
anonymous
  • anonymous
now we have: h' = 0.2 ft/sec we need to find r'
anonymous
  • anonymous
do i just plug in
anonymous
  • anonymous
yes :) but we need to find r' now
anonymous
  • anonymous
\[V' = 2 \pi rr' h'\] we have h' , but we need to find r' to calculate V' = rate of volume increase
anonymous
  • anonymous
how do i do that? :(
anonymous
  • anonymous
hold on :)
anonymous
  • anonymous
thx
anonymous
  • anonymous
you need to find a relationship between r and h so r/h = r'/h'
anonymous
  • anonymous
thats where im having problem for all the problems
anonymous
  • anonymous
cross mulitply and you'll get: r' = rh'/r
anonymous
  • anonymous
sorry! wait you'll get: r' = rh'/h :)
anonymous
  • anonymous
are you with me soo far?
anonymous
  • anonymous
yes :)
anonymous
  • anonymous
now plug : r =3 ft h = 6ft h' = 0.2ft/sec r' = (3)(0.2)/6 = 0.1 ft/sec
anonymous
  • anonymous
we have found r' now, let's go back to V'\[V' = 2 \pi rr'h'\] so, V' = 2(3)(0.1)(0.2) pi = 0.377 ft^3/sec
anonymous
  • anonymous
Correct me if I'm wrong please
anonymous
  • anonymous
OMG this makes so much sense now
anonymous
  • anonymous
but the website marked it wrong :(
anonymous
  • anonymous
why?
anonymous
  • anonymous
I guess there's a mistake, but that's the idea, maybe in calculation?
anonymous
  • anonymous
ok
anonymous
  • anonymous
did you get the idea?
anonymous
  • anonymous
one qquestion
anonymous
  • anonymous
sure :)
anonymous
  • anonymous
where did u get \[V \prime = 2\pi r r \prime h \prime \]
anonymous
  • anonymous
you derive with respect to r and h :)
anonymous
  • anonymous
you want to know how is the volume increasing when both the radius and height is changing, that's the story of the related rated problem
anonymous
  • anonymous
oooooh...im sorry can u show me one more problem
anonymous
  • anonymous
hmmmm, let's say we have a circle of radius = 2 m, and the radius is decreasing at 0.5 m/sec. How much will the circle's area increase ?
anonymous
  • anonymous
I'll give you advise, whenever you see ( m/sec) or anything with respect to time it's something' which in this case is the r' = 0.5m/sec
anonymous
  • anonymous
so what is the given?
anonymous
  • anonymous
we have : - R = 2 m - R' = 0.5 m/sec and we know the formula of the Area of the circle which is: A = pi r^2, right?
anonymous
  • anonymous
uhhuh
anonymous
  • anonymous
Now , you want to know how much is the area increasing with respect to R, since R is increasing :) so you find the derivative of it which will be : A' = 2 pi rr'
anonymous
  • anonymous
so when exactly do i start pluging in numbers?
anonymous
  • anonymous
right now, after you find the derived formula, start pluggingthe numbers :)
anonymous
  • anonymous
okay ...these are pretty simple compared to the ones i have on hw :'(
anonymous
  • anonymous
Like this problem, they want to know how much is the area increasing , we got the formula so the answer is: A' = 2(2)(0.5) pi = 2 pi = 2.68 m^2/sec :) So the area is increasing at 2.68 m^2/sec
anonymous
  • anonymous
Lol, when you understand the small idea, you'll be able to figure out the bigger idea :)
anonymous
  • anonymous
did you understand my problem?
anonymous
  • anonymous
yes but how would i approach towards a hemisphere problem
anonymous
  • anonymous
think about it, write down the given on one side, and the RTF(required to find) on the other side, then SKETCH! To test your understanding , you've got to sketch what they give you to be fully understand what they want :)
anonymous
  • anonymous
to fully*
anonymous
  • anonymous
1) write the given and what you need to find 2) sketch 3) write down the general formula that you're going to use :)
anonymous
  • anonymous
^_^
anonymous
  • anonymous
ok :)
anonymous
  • anonymous
good luck ! You're a smart student, you can figure it out :)
anonymous
  • anonymous
you got the small idea, you'll be able to solve any bigger ideas now . They are not even big, they are small ideas that got stretched ^_^, don't let the problem boss u, YOU ARE THE BOSS!
anonymous
  • anonymous
lol..thx
anonymous
  • anonymous
np :) Give it a try once more. ^_^

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